Total vs partial derivatives

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Partial derivatives involve only individual components. Total derivatives are the derivatives of an objective or constraint with respect to design variables.

0:00 - Intro
0:40 - What are partial derivatives?
1:40 - What are total derivatives?
2:44 - Totals can be computed from a mix of partials
5:32 - Conclusion

Accompanying course page:

TODO: add linked lectures as they're developed
  1. OpenMDAO
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your intro just earned you a sub right of the bat

brickie
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How would you recommend developing these partials and handing them over to OpenMDAO? Would you suggest a symbolci python package to compute them?

Equally, I have run a few loops in OpenMDAO without informing the partials at all, and it still solves the problem. Is it developing partials for me automatically?

Thanks!

AeroStark